Google will automatically find and index your site, you don't need to do anything for that to happen.
Before you start thinking about promoting your site you should spend time on developing it. Content is king when it comes to search engine success; you'll do even better in the rankings if your subject matter is unique, or at least uncommon. Populate your site with interesting content, and then encourage other sites to link in to you.
After you've done all that, make frequent changes in the text and image content, ensure that your site's navigation works perfectly,and you'll be on your way. Google knows a good site when it sees one.